How to Use the Percentage Calculator
This calculator handles five percentage scenarios: finding a percentage of a number, calculating what percentage one number is of another, measuring percentage change between two values, finding the whole from a known part and percentage, and computing percentage difference between two values.
Calculation Modes
% of — What is X% of Y?
Enter a percentage and a total number to find the portion that percentage represents.
Formula: Result = (Percent / 100) × Total
Example: What is 20% of 150?
- Percentage: 20%
- Of Number: 150
- Result: 30
Example: What is 8.5% of 2,400?
- Result: 204
Find % — X is what % of Y?
Enter a part and a total to calculate what percentage the part represents.
Formula: Percentage = (Part / Total) × 100
Example: 45 is what % of 180?
- Part: 45
- Of Total: 180
- Result: 25%
Example: 72 is what % of 60?
- Result: 120%
Change — Percentage Increase or Decrease
Enter an original value and a new value to calculate the percentage change. Negative results indicate a decrease; positive results indicate an increase.
Formula: Change = ((To - From) / |From|) × 100
Example: Price increased from $50 to $65:
- From: 50
- To: 65
- Result: 30% (increase)
Example: Stock dropped from $80 to $68:
- From: 80
- To: 68
- Result: -15% (decrease)
Example: Temperature rose from -10°C to 5°C:
- From: -10
- To: 5
- Result: 150% (increase)
Whole — Find the Whole from a Part and Percentage
Enter a known part and the percentage it represents to find the total whole.
Formula: Whole = Part / (Percent / 100)
Example: 30 is 25% of what number?
- Part: 30
- Percent: 25%
- Whole: 120
Example: $450 is 15% of a total budget:
- Part: 450
- Percent: 15%
- Whole: 3,000
Diff — Percentage Difference Between Two Values
Enter two values to calculate how far apart they are as a percentage of their average. This is commonly used in scientific and statistical comparisons.
Formula: Difference = |V1 - V2| / ((V1 + V2) / 2) × 100
Example: Difference between 50 and 70:
- Value 1: 50
- Value 2: 70
- Difference: 33.333333%
Example: Difference between 120 and 150:
- Difference: 22.222222%
Precision and Notation Settings
Use the settings bar above the tabs to control how results display:
- Decimal places: Adjust from 0 to 16 decimal places (default is 8)
- Notation: Switch between auto, fixed, exponential, and engineering notation (default is auto)
Your decimal places and notation settings save to your browser automatically. When you return to this calculator, your last chosen format loads without needing to adjust it again.
Common Use Cases
Calculating a Tip
You want to leave an 18% tip on an $85 bill:
- Switch to % of
- Enter 18 as Percentage
- Enter 85 as Of Number
- Result: $15.3
Finding a Discount Amount
A $200 jacket is 30% off:
- Switch to % of
- Enter 30 as Percentage
- Enter 200 as Of Number
- Result: $60 (this is your discount)
Measuring Sales Growth
Revenue grew from $12,000 to $15,000:
- Switch to Change
- Enter 12000 as From
- Enter 15000 as To
- Result: 25% (increase)
Reverse-Calculating a Total Budget
You spent $840 on marketing, which is 12% of your total budget:
- Switch to Whole
- Enter 840 as Part
- Enter 12 as Percent
- Whole: $7,000 (this is your total budget)
Grade Percentage
You scored 38 out of 50 on a test:
- Switch to Find %
- Enter 38 as Part
- Enter 50 as Of Total
- Result: 76%
Comparing Two Measurements
Two labs measured a sample as 4.2g and 4.8g:
- Switch to Diff
- Enter 4.2 as Value 1
- Enter 4.8 as Value 2
- Difference: 13.333333%
Tips for Accurate Calculations
- % of and Find % are inverses: The same two numbers produce different results depending on which mode you use
- Change mode allows negatives: The From and To fields accept negative values for temperature or financial changes
- Change divides by absolute From: The formula uses |From|, so a change from -50 to -25 gives 50% (improvement), not -50%
- Whole mode requires positive percent: Finding a whole from 0% would require infinite division; the calculator blocks this
- Difference uses the average as baseline: Diff compares against the midpoint, so input order does not matter
- Zero sums block Diff: If value1 and value2 sum to zero (e.g., 5 and -5), the average is zero and division is undefined
Troubleshooting
Required
This appears when a field is left empty. Enter a value in all fields before calculating
Percent cannot be negative
In % of mode, enter a positive percentage or zero. Negative percentages are not valid for this operation
Total must be positive
In % of and Find % modes, the total (or "of" number) must be greater than zero. Division by zero is undefined
Part cannot be negative
In Find % mode, enter a positive part or zero
Cannot divide by zero
In Find % mode, the total cannot be zero. A part of zero is undefined as a percentage
Must be a valid number
In Change and Diff modes, enter a valid number. Non-numeric characters are not allowed
Cannot calculate change from zero
In Change mode, the From value cannot be zero. Percentage change from zero is mathematically undefined
Percent must be positive
In Whole mode, the percent must be greater than zero. A part cannot represent 0% or a negative percentage of any whole
Cannot divide by zero percent
In Whole mode, the percent cannot be zero. A part cannot represent 0% of any whole
Cannot calculate difference with zero sum
In Diff mode, the two values cannot sum to zero (e.g., 10 and -10). Their average would be zero, making division impossible